#isotropic

[tenth-sentence]

He followed the same intellectual path, however, assuming an isotropic and homogenous distribution of matter in the cosmos, and searching for solutions to Einstein's equations that describe the story of this smooth and uniform universe.

"Human Universe" - Professor Brian Cox and Andrew Cohen

[waybackwanderer]

The Isotropic Media Group Oct 1996 Archived Web Page

[katieprattartist]

My titles have become more esoteric over time… this one is comparatively self-explanatory 1. Isoberg 2003 #oiloncanvas 200 x 180cm There are skeins of #lemonyellow dotted lines joining similarities across the #pictureplane Voluminous lumps of #paint as well as pigment stencils of splashes lie on the raw #canvas Raw #pigment and fat #oilpaint 2. Cover of #anmagazine March 2004 3. #detail of Isoberg 9 #oilpainting #contemporaryart #contemporarypainting #abstractpainting #abstraction #isotropic #artistsarchive #archive #painting #painter #artist #artistsoninstagram #londonartist #katiepratt #explorepage #artistsnewsletter @anartistsinfo 📸 #RichardKearns https://www.instagram.com/p/CoUsY1godU5/?igshid=NGJjMDIxMWI=

[conceptofjoy]

davesprite looking between john and his corpse on his quest bed. u gonna do anything with that orrrr.

[kilobran]

Love it when my assignment for class is "draw a character" I was gonna do that anyways, so eat that

[hsmagnet]

Mitre Magnet - A Revolutionary Advancement In Precision Magnet

Mitre Magnet ��� A Revolutionary Advancement In Precision Magnet In a significant leap for the magnetics industry, the introduction of the Mitre Magnet is setting new standards for precision and efficiency. This innovative product is designed to cater to the ever-evolving needs of various industrial applications, from manufacturing to scientific research. The Mitre Magnet’s unique configuration and…

[tanadrin]

And God said, "Behold! I have created the fourth primordial force: the weak interaction!"

And the angels all clapped and nodded politely, and there was a long silence; and finally Verchiel, the Angel of Grace, spoke up and asked, "Er, what exactly does it do, O Fashioner?"

And God said, "What do you mean, 'what does it do?' It's the fourth fundamental force of the universe."

And Verchiel said, "You mentioned that. Um. But it's just that the other three sort of have a brand, you know? Gravity helps build large-scale structures, acts over vast cosmic distances, shapes time and space. The strong force is secret, hidden, binding together quarks and all that. Electromagnetism, very cool stuff, somewhere in between. We're all big fans of the whole magnetic monopole double bluff, very clever. But, er. What does this 'weak interaction' do?"

And God said, "It mediates radioactive decay. Sort of."

And Verchiel said, "Radioactive decay? All radioactive decay?"

And God said, "No. Just some kinds."

And Zephaniel, the Chief of the Ishim spoke, and he said, "A whole independent force just to mediate some kinds of radioactive decay?"

And God said, "Well. Not totally independent. Technically it's related to electromagnetism."

And Zephaniel said, "Wait, it's not even a real force?"

And God said, "It's totally a real force. It's just that it's one aspect of a combined electromagnetic and weak force. An electro-weak force, if you will."

And Metatron, the Celestial Scribe, scratched his head at this, but said nothing.

And Cambiel, the Angel of Transformation, said, "Maybe you can walk us through it from the top."

And God Sighed an immense Sigh, and said, "All right, fine.

"So the way it works is that all of space and time is permeated by a field that has imaginary mass."

And Cambiel said, "Imaginary mass, O Generous Provider?"

And God said, "Yes, imaginary mass. It's tachyonic, d'you see?"

And Sarathiel, the Angel of Discipline, said, "Wait a minute, I thought we agreed nothing was going to travel faster than light? All that 'c' business and the whole Lorentz transformation thing. What's happening with that?"

And God said, "Let me finish. The field is tachyonic. The particles in the field all move slower than light."

And Sarathiel had to think about this for a second.

And God said, "The point is, a field with imaginary mass has a non-zero vacuum expectation value."

And this really gave Sarathiel trouble, since he had never been very good at math.

And God, seeing this, went back to explain. "Most fields, like the electromagnetic field, have no effect when they are at their lowest energy state. It's like they're not there at all. If you give a field imaginary mass, then it vanishes only when it's at a very high energy state, and at a low energy state, it has a nonzero value everywhere."

And Sarathiel nodded, but he was confused, because he didn't understand why God would create such a thing.

But Verchiel thought he saw where God was going with this, and he was amazed.

"Truly, you are cunning beyond measure, O Only One Certainly Sound and Genuine in Truth! Only now do I understand your design! For in order to make the universe homogenous and isotropic, it is necessary that all large-scale fluctuations in temperature and mass must be evened out early in the history of the cosmos; and therefore, you have designed a field which will rapidly expand space after the Big Bang, many orders of magnitude in brief moments, and then swiftly and spontaneously decay as it gives up the energy it began with, giving rise to radiation and particles of all kinds as it does, which will condense into the material universe! It is a wonder to behold."

And God said, "What? No. I mean I did, but this isn't the inflaton field I'm talking about. This is something else."

And Verchiel said, "Wait, it's not?"

And God said, "No, I'm going to use a different field to drive cosmic inflation. The properties of this field are totally different."

And now Verchiel was also confused, and lapsed into silence.

And God said, "Like I was saying, this field is a scalar field with imaginary mass, and it does spontaneously decay to a ground state with a non-zero value. But it's not the inflaton field. Instead it combines with the W1, W2, W3, and B bosons."

And Metatron began to flip back through the pages of the Heavenly Record trying to figure out where he'd lost the thread.

And Zephaniel said, "The what bosons?"

And God said, "The W1, W2, W3, and B bosons. I'm sure I mentioned them. You know, the massless bosons?"

And Zephaniel said, "I'm pretty sure we only talked about the W+, W-, and Z0 bosons. All of which you said were going to have mass, O Owner of All Sovereignty."

And God said, "Yes, but this is how they get them, you see. Once this field acquires a nonzero value everywhere, the massless bosons interact with it and get mass. Well, some of them do. They turn into the W+, W-, and Z0 boson. And the photon."

And Zephaniel said, "…and the photon, O Accepter of Invocation?"

And God said, "Well, I did say I was going to unify the electromagnetic force and the weak interaction, didn't I? This is how. Above the critical temperature--right now I'm thinking 10^15 K, but I'm open to feedback on that one--electromagnetism and the weak force act as a single unifying force. Below that temperature, the field gets a nonzero value, you get three massive bosons to mediate the weak interaction, and the photon pops out seperately."

And Zephaniel said, "That seems… a bit overly complicated, doesn't it, O Reinstater Who Brings Back All?"

And God said, "No, it's exactly what we need. Look, that way the W and Z bosons have something to do, but the weak interaction still only travels short distances. Gravity is still the star of the show on cosmic scales, as it were. But now quarks and leptons can swap their flavor!"

And Zephaniel said, rather weakly, "Their… flavor, O Source of Good?"

And God said, "It's this new quantum number I'm trying out, to give the three generations of matter more unique identities."

And Cambiel said, "Three generations of matter? Now I'm really confused."

And God said, "I'm sure I mentioned this. You've got the lightest quarks and leptons, and then two heavier versions of each that can decay into the lighter versions."

And Cambiel said, "What do they do? New kinds of chemistry, is it?"

And God said, "Well, no. Mostly they just decay in a couple microseconds. Or even faster."

And Zephaniel began to rub his temples, and Cambiel sniffed.

And Cambiel said, "This all seems a bit ad hoc to me. Not really the stuff of an elegant and obviously ordered Creation. Why not have four generations of matter? Why not a trillion?"

And God began to grow irritable, and said, "Well, that's not really up to you, now is it? We're going to have three generations of matter, and the electroweak force, and that's that!"

And Zephaniel said, "As long as we are unifying fundamental forces, perhaps we could somehow also unify the electroweak interaction with the strong interaction, or even gravity."

And God hesitated saying, "Well, I haven't decided about that yet. I'm not sure I want gravity to be quantized, you know? Seems to take some of the geometric elegance out of general relativity."

And now it was Zephaniel's turn to sigh, and he bowed his head. "As you wish, O Possessor of Authority of Decisions and Judgement."

[mpcomagnetics]

Where are Samarium Cobalt Magnets Useful?

Where are Samarium Cobalt Magnets Useful? All the information you need to be an informed buyer of Samarium Cobalt Magnets right here, for free! Samarium Cobalt Magnets are among the second most common rare earth magnets. They can be used in temperatures on both the hottest and coldest end of the spectrum (although some swings of temperature have more impact on SmCo magnets than others). Most…

[sukimas]

give me 2 million dollars

i made the empire state building with magnets and radio waves

[willigula]

Isometric Systems in Isotropic Space. Map Projection: Snail, by Ágnes Dénes, 1974

[hsmagnet]

High End Magnets for Particle Accelerators

High End Magnets for Particle Accelerators High End magnets are often used in very sensitive measurement and laboratory equipment. The major difference between standard magnets and high end magnet is the high level of narrow specifications and documentations made on each magnet. In order to be able to deliver high end magnets HSMAG have build up strong competencies within magnetic measurements…

[rock-swag-tournament]

Mineral Swag Round 3: Gems

Aquamarine is the blue variety of beryl, which is a cyclosilicate mineral with beryllium in it. Aquamarine is named for sea water - literally aqua marina aka "marine water." It is a beautiful gemstone and the March birthstone.

Garnet is the January birthstone and actually comes in MANY colors. It is commonly red or pink but can be green or orange as well, depending on the garnet variety you’re talking about. It naturally forms dodecahedra and is an isotropic mineral so it goes “extinct” (turns opaque) under cross polarized light. Pictures of this are in previous rounds!

Garnet is, by far, my favorite mineral because of almandine garnets (shown) are such a beautiful deep red color. Plus they're a metamorphic mineral! So they form in rocks like schist and gneiss. Aquamarine, for anyone interested, forms in igneous rocks like granite.

[mpcomagnetics]

The Complete Guide of Neodymium Magnets

The Complete Guide of Neodymium Magnets NEODYMIUM MAGNETS: THE STRONGEST COMMERCIALLY AVAILABLE MAGNETS Neodymium Magnets are really Strong Magnets made by an alloy of neodymium, iron and boron (NdFeB). Neodymium is a rare-earth element (REE), also called rare-earth metal or (in context) rare-earth oxide. Even at their smallest size Neodymium Magnets have a Really High Magnetic Strength. They…

[thomasmartinnutt]

Agnes Denes. The Isometric Systems in Isotropic Space-Map Projections. The Doughnut, 1980

[materialsscienceandengineering]

Van der Waals equation

Named for physicist Johannes Diderik van der Waals, the van der Waals equation is an adaptation/extension of the ideal gas law for non-ideal gases. It introduces two fitting parameters, commonly written as lowercase a and b, that must be determined experimentally for each gas. The first constant, a, corrects for intermolecular forces, while the second constant, b, adjusts the volume occupied by the gas molecules themselves. The constants for many gases are already known, though they can vary depending on the conditions. The van der Waals equation is not a perfect solution, assuming spherical gas molecules and isotropic intermolecular forces, but it can provide useful estimations for real gases, more accurate than the ideal gas law alone.

Sources/Further Reading: (Images source - Wikipedia) (LibreTexts) (Engineering Toolbox) (Modern Physics) (SUNY at Binghamton) (University of Oxford)

[tensorboi]

Why is the Pythagorean theorem true, really? (and a digression on p-adic vector spaces)

ok so if you've ever taken a math class in high school, you've probably seen the Pythagorean theorem at least a few times. It's a pretty useful formula, pretty much essential for calculating lengths of any kind. You may have even seen a proof of it, something to do with moving around triangles or something idk. If that's as far as you've gotten then you are probably unbothered by it.

Then, if you take a math class in university, you'll probably see the notion of an abstract vector space: it's a place where you can move things and scale them. We essentially use these spaces as models for the physical space we live in. A pretty important thing you can't do yet, though, is rotate things or say how long they are! We need to put more structure on our vector spaces to do that, called a norm.

Here's the problem, though: there are a *lot* of different choices of norm you can put on your vector space! You could use one which makes Pythagoras' theorem true; but you could also use one which makes a³ + b³ = c³ instead, or a whole host of other things! So all of a sudden, the legitimacy of the most well-known theorem is called into question: is it really true, or did we just choose for it to be true?

And if you were expecting me to say "then you learn the answer in grad school" or something, I am so sorry: almost nobody brings it up! So personally, I felt like I was going insane until very recently.

(Technical details: the few that do bring it up might say that the Pythagorean norm is induced from another thing called an inner product, so it's special in that way. But also, that doesn't really get us anywhere: you can get a norm where a⁴ + b⁴ = c⁴ if you are allowed to take products of 4 vectors instead!)

How is this resolved, then? It turns out the different norms are not created equal, and the Pythagorean norm has a very special property the others lack: it looks the same in every direction, and lengths don't change when you rotate them. (A mathematician would say that it is isotropic.) Now, all of a sudden, things start to make sense! We *could* choose any norm we like to model our own universe, but why are we going to choose one which has preferred directions? In the real world, there isn't anything special about up or down or left or right. So the Pythagorean norm isn't some cosmic law of the universe, nor is it some random decision we made at the beginning of time; it's just the most natural choice.

But! That's not even the best part! If you've gone even further in your mathematical education, you'll know about something called p-adic numbers. All of our vector spaces so far have been over the field of real numbers, but the p-adic numbers can make vector fields just as well. So... are the Pythagorean norms also isotropic in p-adic spaces? Perhaps surprisingly, the answer is no! It turns out that the isotropic norms in p-adic linear algebra are the ∞-norms, where you take the maximum coordinate (rather than summing squares)! So the Pythagorean theorem looks very different in p-adic spaces; instead of a² + b² = c², it looks more like a^∞ + b^∞ = c^∞.

If you're burning to know more details on this, like I am right now as I'm learning it, this link and pregunton's linked questions go into more details about this correspondence: https://math.stackexchange.com/questions/4935985/nature-of-the-euclidean-norm

The interesting thing is that these questions don't have well-known answers, so there is probably even more detail that we have yet to explore!

tl;dr: the pythagorean theorem is kind of a fact of the universe, but not really, but it kinda makes sense for it to be true anyway. also we change the squares to powers of infinity in p-adic numbers and nobody really knows why